ARGUMENT

The term argument in ordinary discourse has several meanings:—(1) It is used
for the premises in contradiction to the conclusion, e.g., "the conclusion which
this argument is intended to establish is," &c.; (2) it denotes what is a
course
or series of arguments, as when it is applied to an entire dissertation; (3)
sometimes a disputation or two trains of argument opposed to each other; (4)
lastly, the various forms of stating an argument are sometimes spoken of as
different kinds of argument, as if the same argument were not capable of being
stated in various ways (Whately, Logic, app. I.).

"In technical propriety argument cannot be used for argumentation, as Dr Whately thinks, but exclusively for its middle term. In
this meaning, the word (though not with uniform consistency) was employed by
Cicero, Quintilian, Boethius, &c.; it was thus subsequently used by the Latin
Aristotelians, from whom it passed even to the Ramists; and this is the meaning
which the expression always first, and most naturally, suggests to a logician"
(Sir W. Hamilton, Discussions, p. 147).

In this sense the discovery of arguments means the discovery of middle terms.

Argument (The Indirect).—It is opposed to the Ostensive or Direct. Of
Indirect
arguments several kinds are enumerated by logicians:—

Argumentum ad hominem, an
appeal to the principles
or consistency of an opponent.

Argumentum ad verecundiam, an appeal to our reverence for some
respected authority.

Argumentum ad populum, an appeal to the passions
and prejudices of the multitude.

Argumentum ad ignorantiam, an argument founded
on
the ignorance of an adversary.

Argumentum per impossibile, or Reductio ad absurdum, is the proof of a conclusion derived from the
absurdity of a contradictory supposition.

These arguments are called Indirect, because the conclusion
that is established is not the absolute and general one in question,
but some other relative and particular conclusion, which the
person is bound to admit in order to maintain his consistency.
The Reductio ad absurdum is the form of argument which more
particularly comes under this denomination. This mode of
reasoning is much employed in geometry, where, instead of
demonstrating what is asserted, everything that contradicts
the assertion is shown to be absurd. For, if everything which
contradicts a proposition is absurd, or unthinkable, the proposition itself must
be accepted as true.